Hi everyone, I have a doubt regarding normal random variables. I know it could really easy to solve but still I can't figure this out. So, if you have to sum to gaussian variable as follows: aN(0,1)+bN(0,1) where a and b are constant we can proceed as follows: aN(0,1)+bN(0,1)=N(0,a^2)+N(0,b^2)=N(0,a^2+b^2) why is this different from this: aN(0,1)+bN(0,1)=(a+b)N(0,1)=N(0,(a+b)^2) which one of the two approaches is correct? Thanks
1st approach is correct..coz N(0'1) is a distribution variable but in second approach its been assumed as algebric variable... so its not sum of distribution but its sum of variable of a distribution that has algebric properties
